Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+4y &= 7 \\ x-6y &= -7\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-6y = -x-7$ Divide both sides by $-6$ to isolate $y$ $y = {\dfrac{1}{6}x + \dfrac{7}{6}}$ Substitute this expression for $y$ in the first equation. $4x+4({\dfrac{1}{6}x + \dfrac{7}{6}}) = 7$ $4x + \dfrac{2}{3}x + \dfrac{14}{3} = 7$ Simplify by combining terms, then solve for $x$ $\dfrac{14}{3}x + \dfrac{14}{3} = 7$ $\dfrac{14}{3}x = \dfrac{7}{3}$ $x = \dfrac{1}{2}$ Substitute $\dfrac{1}{2}$ for $x$ back into the top equation. $4( \dfrac{1}{2})+4y = 7$ $2+4y = 7$ $4y = 5$ $y = \dfrac{5}{4}$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = \dfrac{5}{4}$.